A general and fast procedure for determining the complex anisotropic and dispersive permittivity for materials with anisotropy along the permittivity tensor diagonal and in-plane off-diagonal is presented. The procedure extracts the anisotropic tensor elements from co- and cross-polarized free-space transmission measurements of a material slab of arbitrary thickness. Numerical studies involving simulated transmission data are presented to demonstrate the validity and accuracy of the approach. Measurements of a known isotropic dielectric and two engineered anisotropic specimens were used to further validate and demonstrate the accuracy and capability of the procedure.